FEBRUARY 1992
11
On inferringhybridityfrommorphologicalintermediacy
Paul Wilson'
Summary
Wilson, P.: On inferring hybridity from morphological intermediacy. - Taxon 41: 11-23.
1992. - ISSN 0040-0262.
The type of intermediacy that separates hybridity from divergence is not multivariate
intermediacy;it is the coincidence of intermediate characterstates. For the purpose of showing hybridity,analyses should distinguish between the two types of intermediacy.(1) Hybrid
indices fail to do so. (2) Principal components analysis does so only in an ambiguous way.
(3) Pictorialized scatter diagrams properly present the evidence for an interpretationthat is
intuitive. (4) Counting charactersas intermediate or not-intermediate is an explicit approach
that allows for statistical evaluation given that certain assumptions are made. Simulated
data representing hybridity and divergence are presented to illustrate each method and to
provide a prototype of how to document hybridity using the favored methods.
Hybridization results in intermediacy between parents in many characters. Several
methods are in common usage for presenting intermediacy to demonstrate hybridity
(literatureto be reviewedin Discussion). 'Hybrid indices' and 'principal components
analysis' have been repeatedly used in documenting hybridity.Although other researchers have criticized these methods for being statistically biased, I believe them to be
fundamentally inappropriate in that they do not show the type of intermediacy that is
unique to the results of hybridization. Two other approaches, 'pictorialized scatter
diagrams' and what I call the 'charactercount procedure'are appropriate. I will refine
these two methods.
To show that a plant is of hybrid origin means to distinguish that possibility from
the alternative, which is origin through divergence (Wagner, 1969). Consider Fig. I
and 2, which show contrasting historical scenarios resulting in contrasting character
patterns. Fig. 1 illustrates a kind of divergence where ancestral species did not go
extinct - I call the result a 'phyletic series! In Fig. la, a new species divergedacquiring
pigment in its knobs; in Fig. ib, a second new species diverged with an enlargement of
its central spot. Fig. 2 illustrates hybridization - I call the result a 'reticulate series! In
Fig. 2a, there are two species that have diverged in spine length and intensity of
shading; in Fig. 2b, they hybridize, and the new form is intermediate in both
characters.The central species of a phyletic series (B) resemblesthe end species (A and
C) in separate characters. The central species of a reticulate series (F) splits the difference between the conditions of the end species (D and E) in each character.These
are two very different kinds of intermediacy: overall intermediacy, and characterby-characterintermediacy.Methods that fail to discriminate between the two types of
intermediacy are not useful in distinguishing hybridity from divergence,in contrast to
methods that specifically demonstrate character-by-characterintermediacy.
Although the figures illustrate only two characters each, an inference of hybridity
should be based on the number of charactersthat are intermediate, and two characters
would not be considered strong evidence. This is because it is possible for there to be
Department of Ecology and Evolution, State University of New York, Stony Brook, NY 11794, U.S.A.
TAXONVOLUME41
12
deviations from the ideal difference between phyletic and reticulate series, for at least
three reasons.
(1) For any one character,a phyletic series may look like a reticulate series because
there have been evolutionary changes in adjacent segments of the phylogeny. For
instance, a species with small leaves might give rise to a second species with large
leaves, and that second species might give rise to a third species with very large leaves.
To resolve this uncertainty, examine many separate characters. A large number of
characters is important because it is not reasonable to invoke the same directional
trend in different characters. The distinctness of the characters is important because
unrecognized pleiotropic or functional character correlations will mislead one into
assuming more genetic intermediacy than actually exists.
(2) A reticulate series may deviate from the expected pattern when there is extreme
dominance or epistasis. The expectation of intermediacy is based on an assumption
that most alleles combine with a predominantly additive effect. To the extent that
there is dominance or epistasis, it tends to hide reticulate series. Unless one knows the
genetic basis of character expression (as for allozymes), nothing can be done about
this problem since the same pattern results from divergence as from hybridity (see
Rieseberg & al., 1988 for an analysis of molecular data). One simply must make an
interpretation based on as many characters as possible. Inevitably, some characters
will not be intermediate in any hybrid.
(3) Breeding past the F, generation, especially backcrossing, may alter a pattern of
reticulate intermediacy. Recombination of alleles will to some extent (depending on
the genetics), lead to the expression of parental rather than medial character states.
Unless there is polyploidization, subsequent sexual reproduction tends to obscure
reticulateseries. The morphological approach discussed here works best for situations
in which most of the hybrids are F, 's or polyploid derivatives (McDade, 1990; contra
A
A
B
la
B
C
lb
Fig. 1. Idealized scenario envisioned for the origin of a phyletic series. In la, species A and B
diverged in knob pigmentation. In lb, species C diverged from species B in central spot size.
species B shares some characterswith species A and others with species C.
FEBRUARY 1992
13
Funk, 1985); more complex origins might be better resolved by knowledge of
molecular genetic markersthroughout the ranges of the species involved.
Despite these problems, systematists have a long record of successfully identifying
hybrids as such. Morphological intermediacy has been a primary criterion. Important
evidence has also come from cytology, sterility determinations, enzyme polymorphisms, teratology, micro-biogeography, and comparison against artificial hybrids
(Wagner,1983). In documenting a case for hybridity,all of these forms of evidence can
be valuable. In this paper, I will critique four methods of showing morphological
intermediacy in terms of their ability to distinguish phyletic from reticulate series.
Data
I wrote two PASCAL programs. Each produces a data set. One program simulates
divergence, and the other simulates hybridization. These simulations allow me to
illustrate the methods to be discussed using data that can be thought of as coming
from a known phyletic series and a known reticulate series.
The divergence program does the following. (1) Species 1 is established, de novo,
having 20 characters,all with a value of 10 units. (2) Species 2 is created from species 1
by divergence in a random selection of 15 of the 20 characters. Each of the 15 is
modified either positively or negatively at random. Each is modified a random
amount on a uniform scale for up to 5 units. Species 1 itself goes unchanged. (3)
Species 3 is subsequently created by divergencein a similar manner, again from species
1 (though divergence from species 2 would still create a phyletic series). The 15
charactersin which species 3 diverges are separately chosen at random, so by chance a
few are the same as were modified in the divergence of species 2. (4) Samples of 50
individuals are drawn from all three species: for each character,the character state of
an individual is made to deviate from its species's value at random on a normal
distribution with a standard deviation of 1 unit. (5) Across species, randomly
generated multipliers between 0.1 and 10 are used to transform the variates out of the
D
D
E
2a
F
E
2b
Fig. 2. Idealized scenario envisioned for the origin of a reticulate series. In 2a, species D and E
have diverged in spine length and pigmentation. In 2b, they hybridize to form species F. Species
F is between D and E in each character.
14
TAXON VOLUME 41
original common units into unit scales unique to each character - this step makes the
data seem more realistic but does not change any of the results.
The hybridization program does the following. (1) Species 4 and species 5 are
established, differing in 15 characters. The amount of the difference is random on a
uniform distribution for up to 10 units; the values range from 5 to 15. (2) For each
character,a dominance factor is randomly generated from a normal distribution with
a mean of 0.5 (no dominance) and a standard deviation of 0.25 (a factor deviating
from 0.5 by 2 standard deviations would result in complete dominance). Results from
a second, higher level of dominance, standard deviation = 0.50, will also be mentioned
below. (3) Species 6 is created by hybridization: one individual from species 4 and one
from species 5 are drawn at a time; for each characteran individual's characterstate is
made to deviate from its species's value at random on a normal distribution with a
standard deviation of 1 unit; the two individuals are crossed - for each character,the
parental character states are added together after being weighted by the dominance
factor associated with that character. This is done 50 times to form a sample of 50
individuals. (4) Samples of 50 deviant individuals are separately drawn from species 4
and from species 5. (5) Across species, the variates of each character are transformed
into unique units as before.
Hybrid index analysis
A hybrid index is a quantity calculated for an individual that places it on a scale made
up of the combined ranges of all the characters(Anderson, 1949). For equal weighting
of characters, variates were rescored such that the new range for each character was
from 0 to 1 and the direction of increase for all characters was uniform: from each
variate, I subtractedthe minimum value for that character;I then divided by the range;
and, depending on the original direction of increase, I did or did not additively invert
the variates of a character around 0.5. Hybrid index values were calculated for each
individual as the mean of transformed variates across all characters.These values were
plotted by frequency.
40
40
3
30
zw
3
4
30
z
: 20
20
0
LI
LL
10
10
0
0
.25
.50
HYBRID INDEX
.75
.25
.50
.75
HYBRID INDEX
Fig. 3. Histogram of hybrid indices for data from the simulated phyletic series; 150
individuals pooled.
Fig. 4. Histogram of hybrid indices for data from the simulated reticulate series; 150
individuals pooled.
FEBRUARY 1992
15
The hybrid index histograms revealan intermediate peak for both the phyletic series
(Fig. 3) and the reticulate series (Fig. 4). What cannot be told from the histograms is
that the intermediate peaks result from different types of patterns. The intermediate
peak in the phyletic series represents overall intermediacy - similarities between the
central species and one end species counteract similarities between the central species
and the other end species. The intermediate peak in the reticulate series represents
character-by-characterintermediacy - many of the characters of the central species
have values between those of the end species. Hybrid indices do not distinguish
hybridity from divergence.
If hybridity is already known, hybrid indices might be useful in flagging individuals
that are not as equally intermediate as others, plants that might be worth studying further (Davis & Heywood, 1963). Hybrid indices are potentially useful in showing
backcrossing, and, when a population is sampled at random, hybrid index histograms
can be used to show the structure of a hybrid swarm. Hatheway (1962) and Goodman
(1967) discuss character weighting for the hybrid index. Gay (1960) provides an
elaboration on hybrid index analysis for comparing populations differing in the
amount of hybridization.
Principalcomponentsanalysis
Principal components analysis is a method whereby the variance in a number of
characters is resolved onto synthetic axes by taking into account the covariance between characters. The first principle components axis is made to explain all the
variance that can be explained in one dimension, the second axis is made to explain
the maximum amount remaining in a second independent dimension, and so on
(Pimentel, 1979). The PRINCOMP STD procedure of SAS (Anonymous, 1985) was
used to determine the placement of individuals on the first two principal component
axes based on standardized characters.
Position on the axes are plotted for the phyletic series in Fig. 5, for the reticulate
series with moderate dominance in Fig. 6, and for the reticulate series with high
dominance in Fig. 7. In all three figures, there is a group that is intermediate between
two other groups on the first axis. In the phyletic series and in the reticulate series with
high dominance there is a separation of groups on the second as well as the first axis.
The results for the two axes can be explained in sequence.
(1) In the phyletic series, characterscovary because characterchanges accumulate in
a lineage as evolution proceeds. Not only do they accumulate within a segment of a
phylogeny - in Fig. 1, the diagonal line between species A and B - they also
accumulate through adjacent segments - through the two diagonals between species
A and C. Thus, character differences between species A and B can be incorporated
into the same axes as differences between species B and C, and for similar reasons one
group is between two other groups in Fig. 5. In a reticulate series, characters covary
and hybrids are intermediate. Here again the three groups are separated on the first
principal components axes, as shown in Fig. 6 and 7. Thus, intermediacy on the first
axis does not distinguish between hybridity and divergence.
(2) In a reticulate series in which every characterconforms to idealized expectations
(alleles of additive effect and no recombination), all useful characters will be correlated - the first axis will explain all the variance among groups, though the second
axis will still explain variance among individuals within groups (Fig. 6). In contrast, in
a phyletic series, the second axis is important as well as the first axis (Fig. 5). This
16
TAXONVOLUME41
reflects the fact that different charactersseparate the central species from each of the
two end species. One might, then, suppose that principal components analysis can be
useful in inferring hybridity not through intermediacy itself but through the sufficiency of the first axis. However, even in a reticulate series, the second axis will often
be important in separating groups; this is because any kind of deviation from
idealized expectations will lead to covariation that is independent of the differences
between parents and the intermediacy of hybrids. For instance, the reticulate series
with high dominance closely resembles the phyletic series (compare Fig. 5 and 7). I do
not recommend this technique, but, if principal components are used to infer
hybridity,the evidence is the sufficiency of the first axis in separatinggroups, not mere
intermediacy.
Principal components may be more useful in finding putatively hybridizing groups,
locating the most likely parent of a known hybrid with several possible parents, or
searching for possible backcrossed plants in a hybrid swarm (Wagner, 1983).
Namkoong (1966) and Smouse (1972) provided refinements on this method and
related techniques for analysis of hybrid swarms. Pimentel (1981) compared various
ordination techniques in terms of how well they separated parents, hybrids, and
2
3
6
5
2
1
1
cn
C)
0
-1
-2
-2?
-3,
-4
-3
-2
-1
0
1
-2
2
-1
1st PCA AXIS
0
1
2
1st PCA AXIS
2
7
1
CX)
Fig. 5. Principal components analysis of
datafromthe simulatedphyleticseries.
0.
"o
Fig. 6. Principal components analysis of
data fromthe simulatedreticulateserieswith
low dominance.
Fig. 7. Principal components analysis of
data from the simulated reticulate series with
high dominance.
-1
-2
-3
-2
-1
0
1st PCA AXIS
1
2
17
FEBRUARY 1992
introgressants (also see Dancik & Barnes, 1975; Adams, 1982). This family of techniques, along with hybrid indices, does not allow one to distinguish between hybridity
and primary divergence.
Pictorialized scatter diagrams
A pictorialized scatter diagram is a graphical presentation of the character states of
individuals, the data being recoded so that it is easy to see character-by-character
intermediacy when it exists (Anderson, 1949). A well-drawn pictorialized scatter
diagram facilitates interpretation. I recommend that the icons at one end of a series be
unadorned (open squares without spines) and those at the other end be ornamented
(filled squares with long spines); reticulate intermediates will then be balanced with a
moderate level of ornamentation (half-filled squares with short spines), whereas
Character 1 Character 2 Character 3 Character 5 Character 7
D -18.8
EJ34.7O -35.7
O -71.8
E -8.06
Q 35.8-41.9 a32.4-34.6
I 18.9-20.9 L 71.9-80.3 1 8.07-9.01
6 42.0-48.1
E 21.0-22.9 LE-80.4-88.7 Y9.02-9.96
30.0-32.3
-[F
-? 23.0-25.0 El- 88.8-97.2 9.97-10.92
27.7-29.9
i 48.2-54.3
S54.4-
--E
-27.6
625.1-
E0-97.3-
p10.93-
30
28
t 26
LJ
124
22
20
50
80
65
6
CHARACTER
Fig. 8. Pictorializedscatterdiagramof datafromthe simulatedphyleticseries.
95
18
TAXON VOLUME 41
phyletic intermediates will be an odd mixture of accentuated and minimized features
(some spines long, others absent). I used seven characterssymbolized as follows: position along the horizontal axis, position along the vertical axis, blackening of the
square, and length for each of four spines. The axis characters are treated as continuous. The others are coded into five classes: the range is divided into seven parts,
then the first two and the last two are pooled, making the three central classes (where
hybrids will fall) more prominent.
Fig. 8 shows a diagram for the phyletic series. Fig. 9 shows one for the reticulate
series. The intermediates of Fig. 8 are unbalanced. The intermediates of Fig. 9 are
orderly. There is no character-by-characterintermediacy in Fig. 8. Hybridity is sup-
Character 2 Character 3 Character 6
D -69.3
n 91.8D -4.84
69.4-77.7
-0 80.7-91.7
O
4.85-5.70
6 77.8-86.2-C0 69.6-80.6 ? 5.71-6.55
W 86.3-94.7-0
58.6-69.5
6.56-7.41
0 94.8-58.5
67.42-
Character 9 Character 10
169.7O 63.3D 57.4-63.2E
64.3-69.6
58.9-64.2
0- 51.6-57.3P
53.5-58.8
D-45.7-51.5y
-45.6
Y -53.4
--
55
45.
i,
(
35.
C)
25-
15
50
80
110
CHARACTER1
Fig. 9. Pictorializedscatterdiagramof datafromthe simulatedreticulateseries.
140
FEBRUARY1992
19
Table1. Character
countprocedure(steps 3 and4) fordatafromthe simulatedphyletic
series. Means? standarddeviationsare presented;samplesizes were50 throughout.
"1
different
from"indicatessignificantly
differencesbetweenspecies 2 or 3 or bothor neither
indicateswhetheror notspecies
based on Tukeymultiple
comparisons."1intermediate?"
1 was between2 and3 forthatcharacter;
thetallyof these indications
is presentedatthe
bottomof the column.Character2 is not shownsince it was not usefulin separating
species 2 and3.
Character
No.
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Species
2
38.90
20.81
24.96
73.15
61.32
8.21
37.56
94.60
42.87
1.86
62.83
21.83
139.60
67.08
25.75
60.29
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
4.464
2.164
2.434
7.378
8.366
0.845
3.105
9.403
4.148
0.216
5.461
2.452
9.345
6.931
2.027
7.183
Species
1
58.11
23.11
24.57
71.50
72.00
8.43
25.99
93.63
42.00
2.40
47.15
22.32
93.48
67.44
23.25
74.49
? 4.847
? 2.496
? 2.067
? 7.135
? 7.610
? 0.894
? 2.579
? 10.113
? 4.118
? 0.215
? 5.219
? 2.463
? 10.211
? 5.821
? 2.595
? 6.131
Species
3
49.93
23.12
23.77
103.75
93.13
11.09
25.77
112.11
21.86
2.33
48.27
23.08
94.99
98.73
23.37
36.68
? 5.590
? 2.630
? 2.227
? 5.836
? 7.023
? 0.908
? 2.427
? 10.319
? 3.936
? 0.278
? 4.306
? 2.342
? 8.752
? 7.005
? 2.329
? 7.130
1 different
from
both
2
neither
3
both
3
2
3
3
2
2
neither
2
3
2
both
1 intermediate?
+
+
+
+
+
+
+
+
8:8
ported in Fig. 9 by a careful inspection of each feature of the central icons compared
to the extreme icons.
The diagrams neither combine varying individuals into groups before considering
deviations in the pattern of different characters(see next section) nor do they combine
characters into indices before considering the deviations in the pattern of different
individuals (as does the method of Wells, 1980) - the viewer is presented with both
kinds of information. The chief limitations of the approach are that (1) the evaluation
of that information remains subjective, and (2) the inclusion of many individuals or
many characters make the diagrams excessively difficult to follow. Still, the diagrams
remain useful in inferring hybridity (Davis & Heywood, 1963). They can also be
employed in showing the degree of intergradation in a hybrid swarm. Warwich & al.
(1989) plot pictorialized icons on principal component axes - this makes for a meaningful adjustment in the position of the icons, but, if the diagrams are done this way, I
recommend more spines be used so that as many charactersare shown individually as
can be done with clarity.
Charactercount procedure
The character count procedure is an approach that has never to my knowledge been
codified in the way I will present it. It is, nevertheless, implicitly part of most papers
claiming to show hybridity. The analysis proceeds by steps rather than being con-
20
TAXONVOLUME41
Table 2. Character count procedure (steps 3 and 4) for data from the simulated
reticulate series with limited dominance (explanation as in Table 1).
Character
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Species
4
67.96 ? 8.376
87.41 ? 8.382
89.77 ? 8.162
75.37 ? 7.322
68.05 ? 8.417
5.86 ? 0.899
26.54 ? 4.326
19.86 ? 2.671
61.67 ? 5.146
68.44 ? 5.943
30.05 ? 3.725
75.85 ? 6.414
53.45 ? 6.767
23.29 ? 2.188
72.70 ? 7.744
Species
6
89.28 ?
97.35 ?
80.04 ?
71.66 ?
66.70 ?
6.42 ?
32.59 ?
27.62 ?
54.49 ?
62.12 ?
35.38 ?
58.81 ?
64.91 ?
21.60 ?
76.29 ?
Species
5
5.925
6.308
5.528
5.443
7.046
0.553
2.664
1.674
3.753
4.732
3.126
4.391
5.042
1.504
6.807
112.09 ? 8.838
104.70 ? 11.628
54.98 ? 7.664
69.47 ? 7.470
84.87 ? 8.000
7.89 ? 0.610
45.54 ? 3.123
30.74 ? 2.709
47.84 ? 4.783
56.40 ? 6.539
45.85 ? 3.973
47.00 ? 5.706
69.40 ? 6.768
20.91 ? 1.928
76.49 ? 6.862
6 different
from
6 intermediate?
both
both
+
+
both
4
+
+
5
both
both
both
both
both
both
both
both
4
4
+
+
+
+
+
+
+
+
+
+
14:1
certed. (1) Place individuals in groups - two putative parental taxa and a putative
hybrid taxon. Grouping can be done subjectively or with numerical techniques. It is
often useful to have knowledge of the parental species in allopatry. (2) Select
characters that separate the parents. Do this without considering how the characters
combine in the putative hybrids. (3) For each character, determine and tabulate
whether or not the value (e.g., mean size, color, etc.) for the hybrids is intermediate.
Report on non-intermediate as well as intermediate characters (some authors have
failed to do this, e.g., Sytsma & Pippen, 1985; Balick & al., 1987). As a matter of
thorough presentation, give group values (means), errorvariance (standarddeviations
and sample sizes), and statistical tests (multiple comparisons) - see Tables 1 and 2. (4)
Count the number of characters that are and that are not intermediate, and judge
whether the coalescence of intermediate character states is too improbable to represent divergence in the same charactersin the same direction. This can be considered a
one-sided sign test of intermediate versus non-intermediate characters.Such a test will
be significant at the 0.05 level when 5 out of 5 charactersare intermediate, or 9 out of
11, 10 out of 13, or 12 out of 16 (Zar, 1984).
Table 1 presents a character count for the simulated phyletic series. Species 1 is
intermediate between 2 and 3 in 8 characters and non-intermediate in 8. There is no
significant deviation (P > 0.05). The hypothesis of divergence is not rejected. Table2
presents a charactercount for the simulated reticulate series. Species 6 is intermediate
between 4 and 5 in 14 charactersand non-intermediate in a single one. The deviation is
very significant (P < 0.01). This pattern would not be expected from divergence, so
the hypothesis of hybridity is accepted. In the case of high dominance (not shown), 12
characters were intermediate, 3 were not. This is significant (P < 0.05). Hybridity is
accepted. The character count procedure successfully distinguishes hybridity from
divergence.
FEBRUARY 1992
21
The null model for the test in step 4 above is divergent evolution in which two
assumptions are made. (1) It is assumed the direction in which a characterchanges in
one segment of a phylogeny has no bearing on the direction in which it changes in
another segment: In Fig. 1, central spot size could have increased or decreased along
either diagonal but whether it increased or decreased in the first diagonal would be
assumed to have no influence on whether it increased or decreased in the second
diagonal. (2) It is assumed that characters are independently free to evolve in either
direction with respect to each other: In Fig. 1, knob pigmentation is assumed to have
not been pleiotropically or functionally correlated with central spot size. If one does
not wish to make the assumptions, intermediate and non-intermediate characters
should still be tallied and reported as if the test were going to be done. This remains
useful since, even when the assumptions are not precisely true, a preponderance of
intermediate character states is still evidence against divergence in favor of hybridity.
The assumptions merely enable one to make a quantitative significance statement,
such as, intermediacy in 9 out of 11charactershas a less than 5 % chance of resulting
from divergent evolution.
Discussion
I have provided a statement and examples of how to and how not to infer hybridity
from morphological intermediacy. Hybrid indices do not distinguish between
divergence and hybridity. Principal components analysis does so in only a limited
manner that is unduly susceptible to the influence of other factors such as dominance.
Pictorialized scatter diagrams properly present the evidence for intuitive interpretation. The character count procedure described here successfully distinguishes
hybridity from divergence. In presenting a case for hybridity, I advise including a
diagram like Fig. 9 and a character count like Table2.
In the systematics of hybrids and their parents, there are a series of increasingly difficult questions that might be addressed using a single data set but with different
analyses: (1) Did a pattern of diversity arise through hybrid origin (hybridity)? (2) Has
there been character recombination through backcrossing toward a parental species
(introgression, narrowly defined)? (3) What are the frequencies of F,'s, backcrosses,
etc. (the structure of a hybrid swarm)? Principal components, hybrid indices, and
similar methods may be useful in analyzing introgression and swarm structure after
one has already demonstrated that hybridization is involved to begin with. Unfortunately, methodological papers on this topic have not made it clear that the methods
for showing introgression or swarm structureare not acceptable for showing hybridity
itself, and that before even trying to show introgression or swarm structure it is
necessary to first show hybridity (e.g., Anderson, 1949; Hatheway, 1962; Namkoong,
1966; Wells, 1980; Pimentel, 1981;Adams, 1982; Brockmann, 1987).
In connection with this lack of clarity in the methodological literature, empirical
reports frequently use analyses erroneously, or at least seem to. There are many
instances in which a naive reader would think that hybrid indices or principal components were being used to demonstrate hybridity,and there are many instances where
a better approach could have been used than was used (e.g., Kirkbride, 1976;Sytsma &
Pippen, 1985; Johns, 1987; Bateman & Farrington, 1987; Kephart& al., 1988; Parnell
& Simpson, 1988; Ness & al., 1990). It is often unclear whether a multivariate analysis
is being used (incorrectly) to show hybridity or whether hybridity has already been
established in an earlier part of a paper and the multivariate analysis is being used to
22
TAXONVOLUME41
show introgression or swarm structure - authors would do well to declare their exact
intentions. Although the presentation of evidence for hybridity often seems poor,
reports of hybridity are probably nevertheless correct because researchers do understand intuitively the difference between character-by-character intermediacy and
overall intermediacy.
Acknowledgements
My ideas were inspired by studying Ribes hybrids with M. Mesler. C. Kurtzhelped with the programing. For manuscript comments, I am also grateful to H. Wagner,R. Sokal, J. Thomson, C.
Janson, and P. Teese. Support was provided by a National Science Foundation Graduate
Fellowship. This is contribution 796 in Ecology and Evolution from the State University of New
Yorkat Stony Brook.
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